Simplify the following expression: $q = \dfrac{-18y + 4}{-12y + 14}$ You can assume $y \neq 0$.
Solution: Find the greatest common factor of the numerator and denominator. The numerator can be factored: $-18y + 4 = - (2\cdot3\cdot3 \cdot y) + (2\cdot2)$ The denominator can be factored: $-12y + 14 = - (2\cdot2\cdot3 \cdot y) + (2\cdot7)$ The greatest common factor of all the terms is $2$ Factoring out $2$ gives us: $q = \dfrac{(2)(-9y + 2)}{(2)(-6y + 7)}$ Dividing both the numerator and denominator by $2$ gives: $q = \dfrac{-9y + 2}{-6y + 7}$